Analytical models of X-shape magnetic fields in galactic halos

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Table 3

Brief description of our two models of three-dimensional, X-shape + spiral magnetic fields in galactic disks.

Model^a	Shape of	Reference^b	Labels of^c	Reference^d	B _r	B _ϕ	B _z
	poloidal field lines	coordinate	field lines	field


Bd	Eq. (87)	r₁ > 0	z₁ (Eq. (88)), ϕ₁ (Eq. (70))	Eq. (77), with Eq. (91)	Eq. (89)	Eq. (68)	Eq. (90)


Dd	Eq. (31)	z₁ = \| z₁ \| sign z	r₁ (Eq. (32)), ϕ₁ (Eq. (70))	Eq. (84), with Eq. (35)	Eq. (82)	Eq. (68)	Eq. (83)

Notes.

^(a)

The free parameters and functions of models Bd and Dd are the same as those of models B and D, respectively (see Table 1 for the free parameters of the poloidal field and Table 2 for the free parameters and functions describing the azimuthal structure). The only difference concerns the power-law index of field lines asymptotic to the z-axis in model B (now restricted to n ≥ 2) or the r-axis in model D (now set to ).

^(b)

Prescribed radius or height at which field lines are labeled by their height or radius, respectively, and by their azimuthal angle.

^(c)

Height or radius of field lines and their azimuthal angle at the reference coordinate.

^(d)

Radial or vertical field at the reference coordinate as a function of field line labels.

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